Paintings

Image by William Fiset, CC BY-SA 4.0

Catherine recently got into painting minimalist art. For her
next painting she wants to create an image with $N$ vertical strips of distinct
colors. She always begins painting her vertical strips on the
left side of the canvas and proceeds to the right side.
However, there are certain pairs of colors Catherine does not
like seeing next to each other. If two such colors are adjacent
in a painting, she considers this painting to be
hideous. Furthermore, there are colors Catherine
prefers over other colors, so when painting she always selects
her most preferred unused color that does not make the painting
(as created so far) hideous, and that allows her to complete a
non-hideous painting. Can you help Catherine find her favorite
painting?

Input

The first line of input contains an integer $T$$(1
\leq T \leq 5)$ denoting the number of test cases that
follow.

The first line of each test case contains one integer
$N$$(3 \leq N \leq 12)$, where
$N$ is the number of
colors/vertical strips Catherine wants her painting to have. On
the second line are $N$
colors ordered in (strictly) decreasing order of preference,
where each color is a string of between $1$ and $20$ lowercase letters (a–z). The third line
contains a positive integer $M$ indicating the number of pairs of
colors that follow. Each of the next $M$ lines contains two space-separated
colors $c_ i$ and
$c_ j$$(c_ i \neq c_ j)$ such that Catherine
does not like seeing color $c_
i$ next to color $c_
j$. No pair of colors will appear on more than one
line.

Output

For every test case output two lines. On the first line
display the total number of paintings Catherine can make that
are not hideous (without consideration for her color
preferences), and on the second line output Catherine’s
favorite painting as a space-separated list of colors
corresponding to the strips in the painting from left to
right.

Note: You are guaranteed that there is always at
least one arrangement of colors Catherine finds non-hideous,
and that the maximum number of paintings Catherine can make is
less than $100\, 000$.